Question Number 212001 by mnjuly1970 last updated on 26/Sep/24
$$ \\ $$$$\:\:\:\:{prove}\:\:{that}: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{k}\in\mathbb{Z}} {\sum}\:\frac{\:\left(−\mathrm{1}\right)^{{k}} }{\:{x}\:+\:{k}\pi}\:=\:\frac{\mathrm{1}}{{sin}\left({x}\right)}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:−−−−−−−−− \\ $$